This large phase III clinical study is studying the effect of vandetanib (ZACTIMA) in treating non-small cell lung cancer (NSCLC). Vandetanib is a new type of agent that targets the blood supply to a cancer tumour (through it's anti-vascular endothelial growth factor receptor (VEGFR) properties) and the tumour cells themselves (through it's anti-endothelial growth factor receptor (EGFR) actions). This study will look at the effects of vandetanib in lung cancer patients who have had their cancer re-appear after treatment with standard chemotherapy.